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Yury Stepanyants
Australian Nuclear Science and Technology Organization Sydney
Nonlinear waves in rotating media
Wednesday 1st, June 14:05-14:55pm,
Carslaw Building Room 373.
Dynamics of nonlinear waves in rotating media is
considered. Particular attention is focused on surface and internal
waves in a stratified ocean under the influence of the Earth's
rotation and on magneto-acoustic waves propagating in magnetized
rotating plasma. A model equation (Ostrovsky's equation) is derived
from the basic set of equations taking into account Coriolis
force. Stationary solutions of this equation are obtained numerically
and by means of asymptotic method, and analyzed in detail. These
include solitary-type solutions (solitons with monotonic and
oscillating tails), complex multisolitons (bound states of coupled
single solitons), as well as periodic waves. It is shown that positive
dispersion (typical for plasma waves), in contrast to negative
(typical for ocean waves), gives rise to specific solitary waves
(Ostrovsky's solitons) having zero total "mass". Dynamics of KdV
solitons in rotating systems is studied and compared with the dynamics
of Ostrovsky's solitons. Results of laboratory modelling of internal
wave dynamics in a rotating tank are presented. Decay laws of solitary
waves due to cylindrical divergence in rotating media are
studied. Dependencies of solitons amplitudes on distance both for KdV
and Ostrovsky's solitons are obtained and compared. Different regimes
of soliton decay are discovered and analyzed in detail. Some estimates
for surface and internal waves in real oceanic conditions under the
influence of the Earth's rotation are presented.
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